Explore topic-wise InterviewSolutions in Current Affairs.

If $f\left(x\right)=alo{g}_e|x|+b{x}^2+x$ has extremum at x = 1 and x = 3, then

Let $f(x,y)=0$ be the equation of a circle. If $f(0,\lambda )=0$ has equal roots $\lambda =2$ and $f(\lambda ,0)=0$ has root $\lambda =\frac{4}{5},5$, then the centre of the circle is

If the tangent to the curve $y^2=x^3$ at $(m^2,m^3)$ is also a normal to the curve at $(M^2,M^3),$ then the value of $mM$ is

Let $S_1$, $S_2$,....... be squares such that for each n≥1, the length

of a side of $S_n$ equals the length of a diagonal of $S_{n+1}$. If the

length of a side of $S_1$ is 10 cm, then for which of the following

values of n is the area of $S_n$ greater then 1sq cm

If $g^{\prime }\left(x^3\right)=e^{x^3}+x^6-x^{-3/2}\forall x>0,g\left(0\right)=0,$ then $g\left(x\right)$ is

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)

Differentiate the following functions with respect to x :

$\frac{1+3^x}{1-3^x}$

What the eccentricity of the hyperbola with its principal axes along the

coordinate axes and which passes through (3,0) and $(3\sqrt{2},2)$

The number of solutions of the equation $2x-\ln (2e^x-3)=c,$ where $c<0$ is

Evaluate the following limit:
$\underset{r\to 1}{\text{lim}}\pi r^2$

Find the
points at which the function f given byhas

(i) local
maxima (ii) local minima

(ii) point of inflexion

If $sinA+sinB=\alpha$ and $cosA+cosB=\beta$ , then write the value of $tan\left(\frac{A+B}{2}\right)$

The angles A, B, and C of a triangle are in A.P. and
b:c = $\sqrt{3}:\sqrt{2},then\angle A=$ .

Which of the following expressions have value equal to four times the area of the triangle $ABC$?

(All symbols used have their usual meaning in a triangle)

If $(1+i\sqrt{2}{)}^x$ = $3^x$, then its only integral solution is

Solve the inequality 2 ≤ 3x – 4 ≤ 5

Let $\lambda \ne 0$ be in $R.$ If $\alpha$ and $\beta$ are the roots of the equation, $x^2-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2-10x+27\lambda =0,$ then $\frac{\beta \gamma }{\lambda }$ is equal to

The line 4x-3y=-12 is the tangent at point A(-3,0) and the line 3x+4y=16 is the tangent at the point B(4,1) to a circle. The equation of circle is .

A person has to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{\text{th}}$ minute. If $a_1=a_2=\cdots =a_{10}=150$ and $a_{10},a_{11},a_{12},\dots$ are in A.P. with common difference as $-2$, then the time (in minutes) taken by him to count all notes, is

Seven people leave their bags outside a temple and returning after worshiping picked one bag each at random. In how many ways at least one and at most three of them get their correct bag?

Find
the inverse of each of the matrices, if it exists.

In a triangle ABC with $\angle A={90}^{\circ }$, P is a point on BC such that PA : PB = 3:4. If AB $\sqrt{7}$ and AC = $\sqrt{5}$, then BP:PC is